Determine if one, both, or neither of the following is a proportion. 168=?2412

, 84=?126
(1 point)
Responses

Neither is a proportion.
Neither is a proportion.

168=2412
only
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction only

168=2412
, 84=126
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction , Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction

84=126
only

1 answer

To determine if either of the given equations is a proportion, we need to express each equation as a fraction and then check if the cross products are equal.

  1. For the first equation, \(168 = 2412\):

    • This can be expressed as \( \frac{168}{1} = \frac{2412}{1} \).
    • Clearly, both sides are not equal, thus it is not a proportion.
  2. For the second equation, \(84 = 126\):

    • This can be expressed as \( \frac{84}{1} = \frac{126}{1} \).
    • Again, both sides are not equal, thus it is also not a proportion.

Now, examining the ratios:

  • The ratio \( \frac{16}{8} \) simplifies to \(2\).

  • The ratio \( \frac{24}{12} \) simplifies to \(2\) as well.

  • Hence, \( \frac{16}{8} = \frac{24}{12} \) is indeed a proportion.

  • The ratio \( \frac{8}{4} \) simplifies to \(2\).

  • The ratio \( \frac{12}{6} \) simplifies to \(2\) as well.

  • Hence, \( \frac{8}{4} = \frac{12}{6} \) is also a proportion.

Thus, we conclude that:

  • \( 168=2412 \) is not a proportion, and \( 84=126 \) is not a proportion.
  • The fractions \( \frac{16}{8} = \frac{24}{12} \) and \( \frac{8}{4} = \frac{12}{6} \) are proportions.

Final Answer: Neither is a proportion.